The technology disclosed herein enables a gripper to shuffle items of removable storage media within a storage apparatus for those items. In a particular embodiment, an apparatus includes a housing for items of removable storage media. A top channel and a bottom channel are shaped to accept and store the items in respective single-file rows via an opening at one end of the rows. The apparatus also includes a shuffler for moving a first subset of the items, including ones of the items located in the bottom channel, towards the opening. When in a resting position, the shuffler includes a catch located at the opening and is connected to a rake at a closed side of the housing at an opposite end from the opening. The rake moves the first subset towards the opening when a gripper grips the catch and pulls outward from the opening. The shuffler returns to the resting position when the gripper releases the catch.